I have a pop of about 70, 4 5x5 field all sown with plump helmet. And I have about 200 seeds. But no plants, and every time a plant does appear, I manage to get a couple of brewing made, then they keep tell me that they need plump helmet spawn.
Those two things aren't related. Brewing takes plants and returns alcohol and seeds (as long as you don't have 200 of one seed type; there's a cap in place). Planting takes seeds and, after some time, returns plants. Also, the phrase you're looking for, if I'm understanding you, is 'I manage to get a couple of brewing jobs done'. Brewing is a job dwarves do, not a thing they make.
Sometimes they also tell me that they need seeds in order to plant seeds (but the stocks are full).
Also the cooking doesn't work, they need "unrotten items".
As mentioned by others, the problem here is that although you have seeds, they're not free to be used. Either they're not in the stockpile because the container they're in is being lugged around, or they're in the stockpile but earmarked to have their containers lugged around.
Now they randomly stop doing their jobs in order to hunt for vermin (I don't have a river, just an underground lake in a cave but I'm worried about letting them fish in it since I just started my militia).
They're starving. Gather some plants on the surface if it's safe to do so, and slaughter any animals you have. Activate the butchery and plant gathering jobs on numerous dwarves -- it's no help to you if all the dwarves who should be producing food are too busy hunting for bugs to get any food made.
How do you suggest I have to do in order to fix it?
Is there a dfhack to remove the rotten food or I have to manually dump away seed by seed?
Seeds don't rot. If the kitchen is enclosed then you can get away with just leaving any rotten food in there, as the clouds of miasma produced by rotten items can't get through doors. But I don't think you even have any rotten food -- if your dwarves are hungry enough to be hunting for vermin, then any food you produce will be gobbled up before it has time to rot.
Make another food stockpile, a fairly large one (11x11 at minimum). Just a general food one (p, f, place stockpile), set to take no barrels at all. This will hoover up any food items you might have lying around. And stop brewing your plump helmets. You need them to feed your dwarves, and the underground water you have will provide your dwarves with liquid until your food stocks are high enough to start turning some of the food into alcohol.